Local Solvability for a Compressible Fluid Model of Korteweg Type on General Domains

In this paper, we consider a compressible fluid model of the Korteweg type on general domains in the N-dimensional Euclidean space for N≥2. The Korteweg-type model is employed to describe fluid capillarity effects or liquid–vapor two-phase flows with phase transition as a diffuse interface model. In...

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Bibliographic Details
Published inMathematics (Basel) Vol. 11; no. 10; p. 2368
Main Authors Inna, Suma, Saito, Hirokazu
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.05.2023
Subjects
Analysis
Banach spaces
Capillarity
Compressibility
compressible fluid
Compressible fluids
Density
Domains
Euclidean geometry
Euclidean space
Fluids
general domain
Geometry, Plane
Geometry, Solid
Korteweg type
local solvability
Mechanical properties
Phase transitions
Regularity
Tensors
Two phase flow
viscous fluid
Japan
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Summary:In this paper, we consider a compressible fluid model of the Korteweg type on general domains in the N-dimensional Euclidean space for N≥2. The Korteweg-type model is employed to describe fluid capillarity effects or liquid–vapor two-phase flows with phase transition as a diffuse interface model. In the Korteweg-type model, the stress tensor is given by the sum of the standard viscous stress tensor and the so-called Korteweg stress tensor, including higher order derivatives of the fluid density. The local existence of strong solutions is proved in an Lp-in-time and Lq-in-space setting, p∈(1,∞) and q∈(N,∞), with additional regularity of the initial density on the basis of maximal regularity for the linearized system.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11102368